Have you ever moved a appliance with a set of hand trucks? Perhaps you should custom design a New cart, That works like a hand truck, roll the cart up to the tanks slightly tilt the tanks forward just enough to slip the carts bottom plate underneath, Then you can tilt the cart slightly back allowing the tanks to settle in place to strap them on, Actually I had made a cart from a set of hand trucks as I have described, Though I cannot provide a Photo, It got where I was rarely using them so I sold the cart and tanks, downsize to the smaller tanks,
Here's you an idea, take the welding cart you already have cut the bottom loose and weld it back in place on a hinge, also have a small steel cable attached to the bottom sides and routing it up along mid-way of the sides of the upright, put you a small winch with a crank handle, a flip of the lock loosens the bottom so that you can slide it under the tanks, now turning the winch handle will easily lift the tanks into the cart,